Accelerometers are electromechanical devices that are widely used to measure acceleration forces due to motion and/or vibration. Capacitive accelerometers may find use in applications including seismic sensing, vibration sensing, inertial sensing and tilt sensing. Capacitive accelerometers are typically implemented as micro electromechanical systems (MEMS) and may be manufactured from a semiconductor material such as silicon. A typical MEMS sensing structure for a capacitive accelerometer comprises a proof mass moveably mounted to a support, with a set of electrode fingers extending from the proof mass being interdigitated with one or more sets of fixed electrode fingers so as to form a differential capacitor. WO 2004/076340 and WO 2005/083451 provide examples of capacitive accelerometers comprising a plurality of interdigitated fixed and moveable electrode fingers extending substantially perpendicular to the sensing direction of the MEMS device. The electrodes of the sensing structure are connected to suitable drive and pickoff electronics, typically in an application-specific integrated circuit (ASIC).
In an open loop accelerometer the electronics are arranged to drive the fixed electrodes with a sine or square wave signal and the proof mass moves under acceleration to provide a pickoff signal that is a rectified voltage appearing on the output. WO 2004/076340 provides an example of an open loop accelerometer. However, open loop accelerometers can have limited performance in terms of bandwidth, linearity and dynamic range.
In an open loop configuration the main requirement for the drive waveforms to ensure accuracy is that the drives reach the same amplitude and have sufficient settling time prior to the pickoff sampling. Variations in the transitions between the two drives do not affect the performance of an open loop sensor as long as there is sufficient settling time, where the mark:space ratio of the drive signal waveform is typically fixed at 50:50 and therefore provides a large time window for settling.
An accelerometer sensing structure designed for open loop operation can also be used in a closed loop configuration by using drive electronics to provide a variable electrostatic force to the electrodes to achieve force rebalancing. WO 2005/083451 provides an example of a closed loop electronic control circuit using pulse width modulation (PWM) of the drive signals. In such a closed loop configuration, the electronics are arranged to drive pairs of the fixed electrode fingers in-phase and anti-phase using PWM signals so that the proof mass is fixed in position by virtue of the electrostatic forces nulling the inertial force due to acceleration. The mark:space ratio of the PWM drive signals can be adjusted to produce a variable rebalance force. Feedback from a pickoff circuit to the PWM drive signal generator causes the length of each PWM pulse to be changed as a function of the pickoff output voltage so as to provide an average electrostatic restoring force maintaining the proof mass at a central null position. In a closed loop configuration, the drive waveform symmetry becomes more important for performance than in open loop operation as the drive signals now provides a measure of the applied acceleration as well as providing the excitation for the pickoff sensor.
In a closed loop configuration, the net value of the rebalancing force is proportional to the applied acceleration. When an electrostatic force transducer is used, the force is proportional to the square of the voltage, such that in a PWM scheme as discussed above, the average force is proportional to the square of the PWM drive signal. This assumes that the amplitude of the PWM voltages is constant at the peak of the drive waveform, and that the acceleration is proportional to the mark:space ratio of the signal. However, in a system such as this there is a ramp time to achieve constant voltages. The ramp time can be characterised by the slew rate, which is the maximum change in voltage per unit time.
The ramp time of the drive voltages can cause errors to be introduced. Having a very short ramp time, while desirable, is impractical, as it requires a high instantaneous current during the ramping phase. However, using a finite ramp time requires the in-phase and anti-phase drive signals to be very well matched. This is because the electrostatic force produced by each transducer varies as a V2 function relative to the pickoff electrode DC voltage, and therefore variations during the ramping phase will change the average DC electrostatic force, so any mismatch would cause a resultant electrostatic force on the proof mass (which is not due to an applied acceleration).
The use of equal but opposite PWM drive signals results in a net balancing force that is directly proportional to the average value of each drive signal. While the electrostatic forces vary as V2, for a fixed drive voltage amplitude the applied restoring force in a PWM scheme is proportional to the average voltage for each drive, as the squared dependency is removed by the use of in-phase and anti-phase drive signals. This equality allows any non-linear terms in the drive signals to be cancelled. Usually, two separate current sources and sinks are used in the driver circuit to produce the respective in-phase and anti-phase signals simultaneously. However, if the in-phase and anti-phase drive signals are not equal and opposite, the non-linear terms will not cancel accurately, causing bias, scale factor and linearity errors. The reference voltage for the PWM signals is therefore critical, as the measurements are taken relative to this reference.
In addition, the PWM drive signals are used to produce pickoff position sensing. The accelerometer output is an AC signal superimposed on a DC offset or bias voltage. In open loop accelerometers and in conventional closed loop accelerometers, the DC offset voltage input to the pickoff amplifier is typically biased mid way between the supply voltage rails to minimise any unwanted electrostatic forces being applied to the proof mass and to allow deviations during the transition period of the drive waveforms. This reduces or eliminates the range of electrostatic force available for rebalancing in closed loop, therefore limiting the dynamic range of the acceleration measurements. This pickoff input DC bias voltage is required to be very stable to ensure no additional errors are introduced. Conventional closed loop and open loop accelerometers try to avoid any net forces being applied to the proof mass by reducing the drive voltage, making it as small as possible in order to reduce the sensitivity of the system to the DC offset of the drive and pickoff signals. For a closed loop PWM based accelerometer, it is therefore advantageous to have the pickoff DC input bias operating at the lower supply rail, at 0V for unipolar electronics such as standard CMOS ASIC processes, to maximise the available rebalancing force.
The present disclosure seeks to reduce or overcome the disadvantages outlined above in relation to driving methods for a closed loop accelerometer.